Dimension Reduction for Multivariate Response Regression Data

Abstract

We consider a regression analysis of multivariate response on a vector of predictors. A major interest in analyzing multivariate data sets is the reduction of dimensionality for visualization the pattern of data structure. In this article we develop dimension reduction methods for reducing the dimensionality of response variables and predictors without loss of information and without requiring a prespecified parametric model. Our method integrates the modification of slice inverse regression and Principal Hessian Directions of Li (1991, 1992) and the most predictable variate method introduced by Li et al. (2003) for dimension reduction in multivariate response regression data. Simulation results for illustration are reported.